A Compendium Of Partial Differential Equation Models
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A Compendium Of Partial Differential Equation Models
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Author : William E. Schiesser
language : en
Publisher: Cambridge University Press
Release Date : 2009-03-16
A Compendium Of Partial Differential Equation Models written by William E. Schiesser and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-16 with Computers categories.
Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.
Methods For Partial Differential Equations
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Author : Marcelo R. Ebert
language : en
Publisher: Birkhäuser
Release Date : 2018-02-23
Methods For Partial Differential Equations written by Marcelo R. Ebert and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Mathematics categories.
This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models. Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results. Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material.
Applied Partial Differential Equations
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Author : J. David Logan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applied Partial Differential Equations written by J. David Logan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems;' The audience usually consists of stu dents in mathematics, engineering, and the physical sciences. The topics include derivations of some of the standard equations of mathemati cal physics (including the heat equation, the· wave equation, and the Laplace's equation) and methods for solving those equations on bounded and unbounded domains. Methods include eigenfunction expansions or separation of variables, and methods based on Fourier and Laplace transforms. Prerequisites include calculus and a post-calculus differential equations course. There are several excellent texts for this course, so one can legitimately ask why one would wish to write another. A survey of the content of the existing titles shows that their scope is broad and the analysis detailed; and they often exceed five hundred pages in length. These books gen erally have enough material for two, three, or even four semesters. Yet, many undergraduate courses are one-semester courses. The author has often felt that students become a little uncomfortable when an instructor jumps around in a long volume searching for the right topics, or only par tially covers some topics; but they are secure in completely mastering a short, well-defined introduction. This text was written to proVide a brief, one-semester introduction to partial differential equations.
An Introduction To Partial Differential Equations
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Author : Michael Renardy
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
An Introduction To Partial Differential Equations written by Michael Renardy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Mathematics categories.
Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.
Partial Differential Equations
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Author : R. M. M. Mattheij
language : en
Publisher: SIAM
Release Date : 2005-01-01
Partial Differential Equations written by R. M. M. Mattheij and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
Textbook with a unique approach that integrates analysis and numerical methods and includes modelling to address real-life problems.
Pde Dynamics
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Author : Christian Kuehn
language : en
Publisher: SIAM
Release Date : 2019-04-10
Pde Dynamics written by Christian Kuehn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Mathematics categories.
This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.
Separation Of Variables For Partial Differential Equations
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Author : George Cain
language : en
Publisher: CRC Press
Release Date : 2005-11-21
Separation Of Variables For Partial Differential Equations written by George Cain and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-21 with Mathematics categories.
Separation of Variables for Partial Differential Equations: An Eigenfunction Approach includes many realistic applications beyond the usual model problems. The book concentrates on the method of separation of variables for partial differential equations, which remains an integral part of the training in applied mathematics. Beyond the usual model problems, the presentation includes a number of realistic applications that illustrate the power and usefulness of the ideas behind these techniques. This complete, self-contained book includes numerous exercises and error estimates, as well as a rigorous approximation and computational tool.
Partial Differential Equations
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Author : Mark S. Gockenbach
language : en
Publisher: SIAM
Release Date : 2005-01-01
Partial Differential Equations written by Mark S. Gockenbach and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
Partial differential equations (PDEs) are essential for modeling many physical phenomena. This undergraduate textbook introduces students to the topic with a unique approach that emphasizes the modern finite element method alongside the classical method of Fourier analysis.
Methods Of Mathematical Modelling
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Author : Thomas Witelski
language : en
Publisher: Springer
Release Date : 2015-09-18
Methods Of Mathematical Modelling written by Thomas Witelski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Mathematics categories.
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
A Compendium Of Partial Differential Equation Models
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Author : William E. Schiesser
language : en
Publisher: Cambridge University Press
Release Date : 2009-03-16
A Compendium Of Partial Differential Equation Models written by William E. Schiesser and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-16 with Mathematics categories.
Mathematical modelling of physical and chemical systems is used extensively throughout science, engineering, and applied mathematics. To use mathematical models, one needs solutions to the model equations; this generally requires numerical methods. This book presents numerical methods and associated computer code in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs). The authors focus on the method of lines (MOL), a well-established procedure for all major classes of PDEs, where the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and makes the computer code easy to understand, implement, and modify. Also, the ODEs (via MOL) can be combined with any other ODEs that are part of the model (so that MOL naturally accommodates ODE/PDE models). This book uniquely includes a detailed line-by-line discussion of computer code related to the associated PDE model.